<p><strong>Figure 7.</strong> As in figure <a href="http://iopscience.iop.org/0953-4075/46/16/164010/article#jpb462676f6" target="_blank">6</a>, for phase+amplitude Gaussian-correlated fluctuations and bandwidths: (a) γ = 15.70Γ<sub>2</sub>; (b) γ = 7.85Γ<sub>2</sub>; (c) γ = 3.92Γ<sub>2</sub>; (d) γ = 1.96Γ<sub>2</sub>; (e) γ = 1.31Γ<sub>2</sub>; (f) γ = 0.98Γ<sub>2</sub>.</p> <p><strong>Abstract</strong></p> <p>Motivated by recent experiments pertaining to the interaction of weak SASE-free-electron-laser (FEL) pulses with atoms and molecules, we investigate the conditions under which such interactions can be described in the framework of a simple phase-diffusion model with decorrelated atom–field dynamics. The nature of the fluctuations that are inevitably present in SASE-FEL pulses is shown to play a pivotal role in the success of the decorrelation. Our analysis is performed in connection with specific recent experimental results from FLASH in the soft x-ray regime.</p>